As it stands after Sunday's episode, the Arya and Sansa storyline back in Winterfell is completely aggravating. Neither of their actions in the last few episodes have made much sense at all for their characters. They're embroiled in some petty feud over a letter that Littlefinger planted for Arya to find. The Stark sisters are playing right into Littlefinger's game—and it seems unlike either of them. Naturally, Game of Thrones fans have been scrambling to find an explanation for their weird behavior.
One very compelling theory is that Arya is deliberately putting on a show for Littlefinger. Perhaps this is all an act, Arya playing the long game until she eventually kills Littlefinger, as Game of Thrones fans have speculated for years. As one Reddit user pointed out, Arya arrived at Winterfell as herself, and has been acting and investigating without a mask:
Arya can change faces, yet she isn't using that ability currently. Why? Because Littlefinger doesn't know she can do that and she WANTS him to see her, Arya Stark, snooping around. Arya has enhanced senses from when she lost her sight, she knows that Littlefinger has been following her. Its also been mentioned that Littlefinger has a certain scent, most likely the only one there who has that type due to his wealth and connections, thus easy for Arya to track with her enhanced sense of smell. Littlefinger doesn't know that Arya was trained by the faceless men. Based on what he knows he can only assume that she has no real training hence why he doesn't question why she's acting so sloppy and obvious.
Which makes sense. If Arya has been trained as an assassin who can change her appearance, why the hell would she sneak into Littlefinger's room as herself? Certainly she wanted to be seen by Littlefinger as Arya sneaking into his room. And, she must have known he was there.
So, what about Arya and Sansa's conversation in Episode Six? That was also pretty clearly a setup. It's unlikely that Arya would just leave those creepy ass masks lying around like that. And it also seemed pretty coincidental that she just walked into the room right after Sansa found them. The key in this scene is that the two were playing the game of faces and Arya made it clear that she was lying about everything. And at the end, she handed Sansa the dagger as gesture of loyalty.
This, it seems only clear, is Arya playing the long game, leading Littlefinger into a false sense of security before she assassinates him. With Littlefinger out of the way, the Knights of the Vale have already made their loyalty to Sansa clear. Another possibility is that after killing Littlefinger, Arya could then get a Littlefinger mask to lead the Knights of the Vale.